\documentclass{article}
\usepackage{pgfplots}
    \pgfplotsset{compat=1.14}    % <-- independent of given value
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        xtick={0,1,5},
        xticklabels={zero,$\alpha$,$\varphi$},
        extra x ticks={-4,-2},
        extra x tick style ={red},
%        extra x tick labels={bla,blub},
    ]
        \addplot+[samples=3] {x^2 - x +4};
    \end{axis}
\end{tikzpicture}
\end{document}
